So you have [LaTeX ERROR: Convert failed]

Now I could be wrong here, but the manufactures claim is based on the accuracy of their cut. How I see if their cut is not so accurate you will get a variety of tubes shorter and longer than the required length so the average will always be pretty much the same. I reckon that you should have .

So want you want is to find c [LaTeX ERROR: Convert failed] note his is a two tailed test.

use to symmetry of the distribution. to get.

[LaTeX ERROR: Convert failed]

then you transform to Z

[LaTeX ERROR: Convert failed]

[LaTeX ERROR: Convert failed]

using tables I get

[LaTeX ERROR: Convert failed]

I'll put some values in now

[LaTeX ERROR: Convert failed]

giving [tex] c = 1.24974[/tex]

and [tex] 2 \mu - c = 1.25026[/tex]

so if the manufactures claim is true, 99% of the time we should get [LaTeX ERROR: Convert failed]

1.2502 is within the range (only just) so we can trust their claim.